Spin dynamics in two-dimensional magnonic crystals

Negli ultimi anni i sistemi magnetici di dimensioni nanometriche sono stati ampiamente studiati sia per le loro proprietà fondamentali che per le molte e potenti applicazioni tecnologiche in cui possono essere inseriti. Tra tutti i sistemi magnetici aventi dimensioni nanometriche, i cristalli magnonici sono quelli che mostrano proprietà molto interessanti poiché possiedono la caratteristiche di poter esser costruiti in una, due o tre dimensioni. Lo scopo di questa Tesi consiste nello studio delle proprietà fondamentali della magnetizzazione in cristalli magnonici mono e multi-materiale. L’analisi è stata condotta con approccio teorico basata su calcoli micro magnetici svolti tramite il metodo della matrice dinamica. Tale metodo permette di calcolare con estrema precisione la dinamica della magnetizzazione in sistemi magnetici periodici grazie alla suddivisione in celle micro magnetiche (di dimensioni inferiori alla lunghezza di scambio del materiale) il sistema. Sono stati studiati quattro diversi reticoli di antidots per analizzare la presenza di modi “soffici” in cristalli magnonici bidimensionali. E’ stato dimostrato che la frequenza di tali modi di spin diminuisce fino a tendere al valore nullo in corrispondenza di un valore critico di campo esterno. Per poter spiegare il fenomeno fisico alla base del “softening” è stato calcolato il campo demagnetizzante che influenza l’andamento della frequenza di queste eccitazioni collettive. Successivamente, un reticolo di antidots con magnetizzazione in piano e fuori piano è stato analizzato per analizzare l’effetto dello stato fondamentale della magnetizzazione sulle curve di dispersione dei modi di spin. Le proprietà della magnetizzazione dinamica sono state studiate anche i cristalli magnonici multimateriali. Diversi sistemi periodici composti da dot circolari immersi in una matrice ferromagnetica sono stati studiati per capire come la posizione e il volume dei dots influenza la propagazione delle onde di spin in tali sistemi. Inoltre, un sistema composto da dot di forma quadrata separato da materiale non magnetico dalla matrice ferromagnetica in cui sono immersi sono stati studiati per comprendere come la presenza di materiale non magnetico modifica lo spettro dei modi di spin. Oltre a questi due tipi di sistemi, è stato analizzato anche un campione composto da due dot di forma ellittica e di materiale diverso separati tra loro. Tale studio è stato fatto sia per lo stato fondamentale con configurazione ferromagnetica che configurazione antiferromagnetica. Infine, è stato possibile classificare i cristalli magnonici come nuova classe di meta materiali grazie all’introduzione di proprietà efficaci che descrivono le onde di spin.Nanopatterned magnetic systems have received a lot of attention in latest years, both from a fundamental point of view and for the several potential technological applications. The most promising candidates are the so called magnonic crystals, that in general are fabricated in one, two, three dimensions. The aim of this Thesis is to investigate from a fundamental point of view the magnetic properties of different kind of magnonic crystals. The analysis is performed by means of a micromagnetic method, called Dynamical Matrix Method, based on a numerical tool named finite-difference technique. The advantage of the Dynamical Matrix Method is to reproduce very accurately the dynamics inside the periodic system due to the subdivision of the sample in nanometric cells of the order of the exchange length. It is very stimulating selecting among the modes resulting from this micromagnetic analysis the relevant modes of physical interest. A systematic investigation of mono-material arrays of antidots is performed in order to analyzed the presence of soft modes in two-dimensional magnonic crystals. It is demonstrated that frequency of particular modes becomes soft at a critical value of external magnetic field. The demagnetizing field felt by soft collective modes is calculated in order to understand the physical phenomena at the bases of the softening. A further investigation concerning the study of out-of-plane and in-plane magnetized antidots lattice is performed. Different dispersion curves have been calculated for collective excitations propagating in the same antidots lattice with different ground-state magnetization. Spin dynamics have been investigated also in magnonic crystals composed of different ferromagnetic materials. The dispersion curves have been calculated for four different magnonic crystals composed of cobalt circular dots embedded into a permalloy matrix in order to understand how the position and the volume of the cobalt influence the band structure of the spin wave modes. A system composed of cobalt and permalloy elliptical dots has been studied in both parallel and antiparallel ground-state magnetization. Magnetic normal modes frequencies have been calculated as a function of the external magnetic field passing from the parallel to the antiparallel grounstate. In addition, the effect of the presence of a non-magnetic spacer has been analyzed by calculating the dispersion curves and the spatial profiles of the collective excitation propagating in five different magnonic crystals composed of squared dots embedded into a permalloy matrix. Finally, some metamaterials properties are introduced for both mono and multi-component systems. By means of these effective quantities the spin dynamics are describes in term of effective quantities. Thanks to these new effect properties, magnonic crystals can be considered as a new class of metamaterials

Metamaterial description of magnonic modes along ΓM direction in a 2D antidot lattice -- Conferenza internazionale

In this paper the metamaterial properties of a two-dimensional magnonic crystal consisting of a periodic array of circular holes (antidots) embedded into a continuous film of permalloy are studied according to micromagnetic calculations based on the dynamical matrix method and to analytical calculations. The magnetic field is applied along the diagonal of the square primitive cell and perpendicularly to the in-plane Bloch wave vector. This geometry corresponds to the high-symmetry direction Gamma M in the reciprocal space. Bragg’s law for magnonic modes at Brillouin zone boundaries is derived by using the notion of effective wavelength. It is also shown that, in the stationary regime, the geometric scattering of collective modes from holes can be regarded as a metamaterial effect having a different meaning with respect to the well-known Bragg diffraction

Sinterconnects: All-Copper Top-Side Interconnects Based on Copper Sinter Paste for Power Module Packaging

Copper sinter paste has been recently established as a robust die-attach material for high -power electronic packaging. This paper proposes and studies the implementation of copper sinter paste materials to create top-side interconnects, which can substitute wire bonds in power packages. Here, copper sinter paste was exploited as a fully printed interconnect and, additionally, as a copper clip-attach. The electrical and thermal performances of the copper-sinter paste interconnections (“sinterconnects”) were compared to a system with wire bonds. The results indicate comparable characteristics of the sinterconnect structures to the wire-bonded ones. Moreover, the performance of copper sinterconnects in a power module was further quantified at higher load currents via finite element analysis. It was identified that the full-area thermal and electrical contact facilitated by the planar sinterconnects can reduce ohmic losses and enhance the thermal management of the power packages